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SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE
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 Title & Authors
SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE
Hwang, Seung-Su;
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 Abstract
It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is isometric to a standard sphere. In this paper we investigate the relationship between the first Betti number and stable minimal surfaces, and study the analytic properties of stable minimal surfaces in M for n
 Keywords
total scalar curvature;critical points;stable minimal surfaces;
 Language
English
 Cited by
1.
THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE,;

대한수학회보, 2013. vol.50. 3, pp.867-871 crossref(new window)
1.
THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE, Bulletin of the Korean Mathematical Society, 2013, 50, 3, 867  crossref(new windwow)
2.
Rigidity of the critical point equation, Mathematische Nachrichten, 2010, 283, 6, 846  crossref(new windwow)
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